What is the percent increase in composite score from first baseline to second baseline administration?

To calculate the percent increase from first to second baseline test administrations, the dataset was manipulated in the following ways to isolate individuals who received two baseline test administrations:

  1. The test_type variable was filtered to only include valid baseline test administrations.

  2. Individuals who completed two baseline tests were identified and all other individuals were removed.

  3. The scores of the individuals’ five composite scores from both baselines were spread across the data set to appear on one row per individual.

  4. Individual data sets for the five composite scores were created to calculate the difference in baseline 2 to baseline 1 administration.

  5. Individuals who did not score higher on the second baseline administration were removed from the individual composite score data sets.

  6. The five composite score data sets were joined together to create a new data frame of individuals who achieved a positve gain on at least one composite score on the second baseline test administration.

  7. This combined data frame was filtered through to identify individuals who achieved a higher score on all five composite tests on the second baseline administration.

18,739 individuals completed two baseline assessments. 18,438 individuals (98.39%) achieved a higher score on at least one out of five composite scores on the second baseline assessment. 1,319 individuals (7.04%) achieved a higher score on all five composite scores on the second baseline assessment.

Five composite scores:

1. Verbal Memory Composite Score

2. Visual Memory Composite Score

3. Impulse Control Composite Score

4. Reaction Time Composite Score

5. Visual Motor Composite Score

Verbal Memory Composite Score - Baseline 2 Composite Score Increase Only

10,441 individuals (55.72%) increased their verbal memory composite score on the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 79 points with a standard deviation of 9.32. The minimum score was observed to be 42, and the maximum score was observed to be 99.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 88.76 points with a standard deviation of 8.12. The minimum score was observed to be 54, and the maximum score was observed to be 100.

Baseline 2 Histogram

Score Increase Summary

The average point increase from baseline 1 to baseline 2 was observed to be 9.76 points with a standard deviation of 6.94 points. The mininum point increase was observed to be 1, while the maximum point increase was observed to be 44.

Score Increase Histogram

Percent Increase Summary

The average percent increase from baseline 1 to baseline 2 was observed to be a 13.14% increase with a standard deviation of a 10.71% increase.

Percent Increase Density Plot

Verbal Memory Composite Score - Increase on all Five Composite Scores

This section summarizes the verbal memory composite score for the 1,319 individuals who achieved a higher score on all five composite scores of the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 79.24 points with a standard deviation of 9.06. The minimum score was observed to be 47, and the maximum score was observed to be 99.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 88.61 points with a standard deviation of 7.85. The minimum score was observed to be 61, and the maximum score was observed to be 100.

Baseline 2 Histogram

Score Increase Summary

The average point increase from baseline 1 to baseline 2 was observed to be 9.37 points with a standard deviation of 6.76 points. The mininum point increase was observed to be 1, while the maximum point increase was observed to be 44.

Score Increase Histogram

Percent Increase Summary

The average percent increase from baseline 1 to baseline 2 was observed to be a 12.57% increase with a standard deviation of a 10.39% increase.

Percent Increase Density Plot

Verbal Memory Paired T-Test Results

A paired T-test was used to compare the mean verbal memory composite scores of all 18,739 individuals who completed two baseline assessments. On average, individuals scored significantly higher on the second baseline test administration (M = 84.74) than the first baseline test administration (M = 82.63), t(18737) = -26.327, p < .01.

Boxplot

T-Test Results

## 
##  Paired t-test
## 
## data:  mem_verbal_1 and mem_verbal_2
## t = -26.327, df = 18737, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.262784 -1.949192
## sample estimates:
## mean of the differences 
##               -2.105988

Baseline 1 Total Descriptive Statistics

Baseline 1 Total Score Histogram

Baseline 2 Total Descriptive Statistics

Baseline 2 Total Score Histogram

Visual Memory Composite Score - Baseline 2 Composite Score Increase Only

11,137 individuals (59.43%) increased their visual memory composite score on the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 68.33 points with a standard deviation of 12.13. The minimum score was observed to be 22, and the maximum score was observed to be 99.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 80.44 points with a standard deviation of 10.71. The minimum score was observed to be 38, and the maximum score was observed to be 100.

Baseline 2 Histogram

Score Increase Summary

The average point increase from baseline 1 to baseline 2 was observed to be 12.1 points with a standard deviation of 8.58 points. The mininum point increase was observed to be 1, while the maximum point increase was observed to be 53.

Score Increase Histogram

Percent Increase Summary

The average percent increase from baseline 1 to baseline 2 was observed to be a 19.74% increase with a standard deviation of a 17.64% increase.

Percent Increase Density Plot

Visual Memory Composite Score - Increase on all Five Composite Scores

This section summarizes the visual memory composite score for the 1,319 individuals who achieved a higher score on all five composite scores of the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 68.61 points with a standard deviation of 11.81. The minimum score was observed to be 22, and the maximum score was observed to be 95.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 81.07 points with a standard deviation of 10.56. The minimum score was observed to be 44, and the maximum score was observed to be 100.

Baseline 2 Histogram

Score Increase Summary

The average point increase from baseline 1 to baseline 2 was observed to be 12.46 points with a standard deviation of 8.7 points. The mininum point increase was observed to be 1, while the maximum point increase was observed to be 44.

Score Increase Histogram

Percent Increase Summary

The average percent increase from baseline 1 to baseline 2 was observed to be a 20.12% increase with a standard deviation of a 17.6% increase.

Percent Increase Density Plot

Visual Memory Paired T-Test Results

A paired T-test was used to compare the mean visual memory composite scores of all 18,739 individuals who completed two baseline assessments. On average, individuals scored significantly higher on the second baseline test administration (M = 76.14) than the first baseline test administration (M = 72.5), t(18738) = -38.047, p < .01.

Boxplot

T-Test Results

## 
##  Paired t-test
## 
## data:  mem_visual_1 and mem_visual_2
## t = -38.047, df = 18738, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.826403 -3.451467
## sample estimates:
## mean of the differences 
##               -3.638935

Baseline 1 Total Descriptive Statistics

Baseline 1 Total Score Histogram

Baseline 2 Total Descriptive Statistics

Baseline 2 Total Score Histogram

Impulse Control Composite Score - Baseline 2 Composite Score Increase Only

7,900 individuals (42.16%) increased their impulse control composite score on the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 5.25 points with a standard deviation of 3.69. The minimum score was observed to be 0, and the maximum score was observed to be 28.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 9.41 points with a standard deviation of 5.27. The minimum score was observed to be 1, and the maximum score was observed to be 30.

Baseline 2 Histogram

Score Increase Summary

The average point increase from baseline 1 to baseline 2 was observed to be 4.15 points with a standard deviation of 3.43 points. The mininum point increase was observed to be 1, while the maximum point increase was observed to be 26.

Score Increase Histogram

Percent Increase Summary

To compute the percent increase of the impulse control composite score, 255 individuals were removed from the data set becuase they obtained a 0 score on the first baseline test administration, which prevents the ability to complete a percent increase calculation. Individuals with a score of 1 or greater on the first baseline test administration were included for this calculation, which slightly skews the data. The average percent increase from baseline 1 to baseline 2 was observed to be a 119.13% increase with a standard deviation of 146.98% increase.

Percent Increase Density Plot

Impulse Control Composite Score - Increase on all Five Composite Scores

This section summarizes the impulse control composite score for the 1,319 individuals who achieved a higher score on all five composite scores of the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 5.17 points with a standard deviation of 3.55. The minimum score was observed to be 0, and the maximum score was observed to be 25.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 9.16 points with a standard deviation of 4.92. The minimum score was observed to be 1, and the maximum score was observed to be 30.

Baseline 2 Histogram

Score Increase Summary

The average point increase from baseline 1 to baseline 2 was observed to be 3.99 points with a standard deviation of 3.19 points. The mininum point increase was observed to be 1, while the maximum point increase was observed to be 23.

Score Increase Histogram

Percent Increase Summary

To compute the percent increase of the impulse control composite score, 50 individuals were removed from the data set becuase they obtained a 0 score on the first baseline test administration, which prevents the ability to complete a percent increase calculation. Individuals with a score of 1 or greater on the first baseline test administration were included for this calculation, which slightly skews the data. The average percent increase from baseline 1 to baseline 2 was observed to be a 114.23% increase with a standard deviation of 140.46% increase.

Percent Increase Density Plot

Impulse Control Paired T-Test Results

A paired T-test was used to compare the impulse control composite scores of all 18,739 individuals who completed two baseline assessments. On average, individuals scored significantly higher on the first baseline test administration (M = 7.41) than the second baseline test administration (M = 6.99), t(18738) = 10.641, p < .001.

Boxplot

T-Test Results

## 
##  Paired t-test
## 
## data:  impulse_control_1 and impulse_control_2
## t = 10.641, df = 18738, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.3393532 0.4926016
## sample estimates:
## mean of the differences 
##               0.4159774

Baseline 1 Total Descriptive Statistics

Baseline 1 Total Score Histogram

Baseline 2 Total Descriptive Statistics

Baseline 2 Total Score Histogram

Reaction Time Composite Score - Baseline 2 Composite Score Increase Only

11,084 individuals (59.15%) improved their reaction time composite score on the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 0.67 points with a standard deviation of 0.11. The minimum score (indicating faster reaction time) was observed to be 0.44, and the maximum score (indicating slower reaction time) was observed to be 2.85.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 0.59 points with a standard deviation of 0.07. The minimum score was observed to be -0.18, and the maximum score was observed to be 1.03.

Baseline 2 Histogram

Score Increase Summary

The average point decrease (indicating better performance for the reaction time composite test) from baseline 1 to baseline 2 was observed to be 0.08 points with a standard deviation of 0.08 points. The mininum point decrease (indicative of better performance) was observed to be 0.01, while the maximum point decrease was observed to be 2.36.

Score Increase Histogram

Percent Increase Summary

The average percent decrease from baseline 1 to baseline 2 was observed to be a 11.36% increase with a standard deviation of a 8.36% decrease.

Percent Increase Density Plot

Reaction Time Composite Score - Increase on all Five Composite Scores

This section summarizes the reaction time composite score for the 1,319 individuals who achieved a higher score on all five composite scores of the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 0.67 points with a standard deviation of 0.12. The minimum score was observed to be 0.44 (indicative of faster reaction time), and the maximum score was observed to be 2.42.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 0.58 points with a standard deviation of 0.07. The minimum score was observed to be -0.18, and the maximum score was observed to be 0.96.

Baseline 2 Histogram

Score Increase Summary

The average point decrease from baseline 1 to baseline 2 was observed to be 0.09 points with a standard deviation of 0.1 points. The mininum point decrease was observed to be 0.01, while the maximum point decrease was observed to be 1.81.

Score Increase Histogram

Percent Increase Summary

The average percent decrease from baseline 1 to baseline 2 was observed to be a 12.48% decrease with a standard deviation of a 9.44% decrease.

Percent Increase Density Plot

Reaction Time Paired T-Test Results

A paired T-test was used to compare the reaction time composite scores of all 18,739 individuals who completed two baseline assessments. On average, individuals demonstrated a faster reaction time on the second baseline test administration (M = 0.62) than the first baseline test administration (M = 0.64), t(18737) = 27.658, p < .01.

Boxplot

T-Test Results

## 
##  Paired t-test
## 
## data:  reaction_time_1 and reaction_time_2
## t = 27.658, df = 18737, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.02063598 0.02378392
## sample estimates:
## mean of the differences 
##              0.02220995

Baseline 1 Total Descriptive Statistics

Baseline 1 Total Score Histogram

Baseline 2 Total Descriptive Statistics

Baseline 2 Total Score Histogram

Visual Motor Composite Score - Baseline 2 Composite Score Increase Only

14,355 individuals (76.60%) increased their visual motor composite score on the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 33.26 points with a standard deviation of 6.46. The minimum score was observed to be 1.13, and the maximum score was observed to be 52.88.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 38.81 points with a standard deviation of 6.3. The minimum score was observed to be 12.05, and the maximum score was observed to be 54.25.

Baseline 2 Histogram

Score Increase Summary

The average point increase from baseline 1 to baseline 2 was observed to be 5.55 points with a standard deviation of 3.97 points. The mininum point increase was observed to be 0.02, while the maximum point increase was observed to be 37.35.

Score Increase Histogram

Percent Increase Summary

The average percent increase from baseline 1 to baseline 2 was observed to be a 18.8% increase with a standard deviation of a 22.17% increase.

Percent Increase Density Plot

Visual Motor Composite Score - Increase on all Five Composite Scores

This section summarizes the reaction time composite score for the 1,319 individuals who achieved a higher score on all five composite scores of the second baseline test administration.

Baseline 1 Summary

The average Baseline 1 score was observed to be 33.18 points with a standard deviation of 6.56. The minimum score was observed to be 1.13, and the maximum score was observed to be 50.8.

Baseline 1 Histogram

Baseline 2 Summary

The average Baseline 2 score was observed to be 39.17 points with a standard deviation of 6.32. The minimum score was observed to be 12.6, and the maximum score was observed to be 53.5.

Baseline 2 Histogram

Score Increase Summary

The average point increase from baseline 1 to baseline 2 was observed to be 5.99 points with a standard deviation of 4 points. The mininum point increase was observed to be 0.02, while the maximum point increase was observed to be 30.

Score Increase Histogram

Percent Increase Summary

The average percent increase from baseline 1 to baseline 2 was observed to be a 20.98% increase with a standard deviation of a 37.46% increase.

Percent Increase Density Plot

Visual Motor Paired T-Test Results

A paired T-test was used to compare the reaction time composite scores of all 18,739 individuals who completed two baseline assessments. On average, individuals scored significantly higher on the second baseline test administration (M = 37.64) than the first baseline test administration (M = 34.15), t(18738) = -89.275, p < .01.

Boxplot

T-Test Results

## 
##  Paired t-test
## 
## data:  visual_motor_1 and visual_motor_2
## t = -89.275, df = 18738, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.569844 -3.416455
## sample estimates:
## mean of the differences 
##                -3.49315

Baseline 1 Total Descriptive Statistics

Baseline 1 Total Score Histogram

Baseline 2 Total Descriptive Statistics

Baseline 2 Total Score Histogram

Paired T-Test Summary

The results of the paired t-tests across all five composite scores for comparison of baseline performance identified that individuals, on average, improved their score on the second baseline test administration of the verbal memory, visual memory, reaction time and visual motor composites. Conversely, individuals were identified to score, on average, significantly higher on the first baseline test administration of the impulse control composite.

Is there a significant difference in baseline test performance for individuals who completed multiple (more than 2) baseline test administrations?

Total Number of Individuals by Number of Baseline Test Administrations Taken

The t-tests in the seciton above compare the performance between individuals who completed two baseline assessments. The number of individuals who completed three, four, and five baseline assessments is large enough to compare differences in performance through the use of a repeated measure analysis of variance (ANOVA).

Table

Plot

Verbal Memory

Three Baseline Tests

For individuals who completed three baseline tests (n = 2,930), performance on the verbal memory composite score was statistically significantly different, F(1.99, 5,822.57) = 236.46, p < .0001, generalized eta squared = 0.03.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. All pairwise comparisons, between baseline test administrations, were statistically significantly different (p < .05). Individuals were identified to achieve the highest verbal memory score on the third baseline assessment (M = 86.52) compared to the second (M = 84.58) and first (M = 82.28) baseline administrations.

Boxplot

Outliers

Of the 54 scores identified to be outliers, none are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn     DFd       F        p p<.05  ges
## 1 baseline_number 1.99 5822.57 223.461 1.06e-93     * 0.03

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Four Baseline Tests

For individuals who completed four baseline tests (n = 420), performance on the verbal memory composite score was statistically significantly different, F(3, 1,257) = 38.53, p < .0001, generalized eta squared = 0.04.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. Five out of six pairwise comparisons, between baseline test administrations, were statistically significantly different (p < .05). Individuals were identified to achieve the highest verbal memory score on the fourth baseline assessment (M = 87.24). This score was significantly greater than the first (M = 82.19) and second (M = 83.70) baseline administrations; however, it was not significantly greater than the third baseline assessment (M = 86.08). All pairwise comparisons between the first, second, and third baseline test administrations were significantly different.

Boxplot

Outliers

Of the 9 scores identified to be outliers, none are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect DFn  DFd      F        p p<.05   ges
## 1 baseline_number   3 1257 38.527 8.09e-24     * 0.039

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Five Baseline Tests

For individuals who completed five baseline tests (n = 78), performance on the verbal memory composite score was statistically significantly different, F(4, 308) = 6.27, p < .0001, generalized eta squared = 0.03.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. Only three out of ten pairwise comparisons were statistically significantly different. Individuals were identified to score significantly greater on both the fourth (M = 84.1) and fifth (M = 85.77) baseline assessment than on the first baseline assessment (M = 80.26). The third signficant difference was identified between the third and fifth baseline administrations, where performance on the fifth baseline assessment was signficantly greater than the third baseline assessment (M = 82.56). The remaining seven pairwise comparisons were not signficantly different.

Boxplot

Outliers

Of the two scores identified to be outliers, neither are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect DFn DFd    F        p p<.05   ges
## 1 baseline_number   4 308 6.27 7.32e-05     * 0.032

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Baseline 5 Summary

Baseline 5 Histogram

Visual Memory

Three Baseline Tests

For individuals who completed three baseline tests (n = 2,390), performance on the visual memory composite score was statistically significantly different, F(1.99, 5,821.49) = 355.72, p < .0001, generalized eta squared = 0.04.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. All pairwise comparisons, between baseline test administrations, were statistically significantly different (p < .05). Individuals were identified to achieve the highest visual memory score on the third baseline assessment (M = 78.75) compared to the second (M = 76.66) and first (M = 72.56) baseline administrations.

Boxplot

Outliers

Of the 54 scores identified to be outliers, none are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn     DFd       F         p p<.05   ges
## 1 baseline_number 1.99 5821.49 355.717 1.23e-145     * 0.041

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Four Baseline Tests

For individuals who completed four baseline tests (n = 420), performance on the visual memory composite score was statistically significantly different, F(3, 1,257) = 54.66, p < .0001, generalized eta squared = 0.05.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. All six pairwise comparisons between baseline test administrations were statistically significantly different (p < .05). Individuals were identified to achieve the highest visual memory score on the fourth baseline assessment (M = 80.50). This score was significantly greater than the first (M = 73.09), second (M = 76.46), and third (M = 78.66) baseline administrations. All pairwise comparisons between the first, second, and third baseline test administrations were significantly different.

Boxplot

Outliers

Of the 4 scores identified to be outliers, none are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect DFn  DFd      F        p p<.05  ges
## 1 baseline_number   3 1257 54.663 3.27e-33     * 0.05

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Five Baseline Tests

For individuals who completed five baseline tests (n = 78), performance on the visual memory composite score was statistically significantly different, F(4, 308) = 9.56, p < .0001, generalized eta squared = 0.04.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. Only three out of ten pairwise comparisons were statistically significantly different. Individuals were identified to score significantly greater on the third (M = 77.27), fourth (M = 78.26), and fifth (M = 79.42) baseline assessment than on the first baseline assessment (M = 71.79). The remaining seven pairwise comparisons were not signficantly different.

Boxplot

Outliers

One score was identified as an outlier and is not considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect DFn DFd     F        p p<.05   ges
## 1 baseline_number   4 308 9.564 2.66e-07     * 0.045

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Baseline 5 Summary

Baseline 5 Histogram

Impulse Control

Three Baseline Tests

For individuals who completed three baseline tests (n = 2,390), performance on the impulse control composite score was statistically significantly different, F(1.98, 5,791.14) = 10.29, p < .0001, generalized eta squared = 0.001.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. Two out of three pairwise comparisons, between baseline test administrations, were statistically significantly different (p < .05). Individuals were identified to achieve the highest impulse control score on the first baseline assessment (M = 7.48) compared to the second (M = 7.33) and third (M = 7.04) baseline administrations. The difference in scores between the first and second baseline administrations was not significant, while the differences between both the first and third and second and third baseline administrations were significant.

Boxplot

Outliers

Of the 404 scores determined to be outliers, 44 are considered extreme.

Normality Assumption

From the plot, the extreme outliers affect the normality of the distribution.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn     DFd      F        p p<.05   ges
## 1 baseline_number 1.98 5791.14 10.294 3.74e-05     * 0.001

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Four Baseline Tests

For individuals who completed four baseline tests (n = 420), performance on the impulse control composite score was not statistically significantly different, F(2.78, 1,163.54) = 0.31, p = .8, generalized eta squared = 0.00031.

Boxplot

Outliers

Of the 60 scores determined to be outliers, 8 are considered extreme outliers.

Normality Assumption

From the plot, the extreme outliers affect the normality of the distribution.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn     DFd     F   p p<.05      ges
## 1 baseline_number 2.78 1163.54 0.314 0.8       0.000308

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Five Baseline Tests

For individuals who completed five baseline tests (n = 78), performance on the impulse control composite score was not statistically significantly different, F(3.28, 252.5) = 0.79, p = .51, generalized eta squared = 0.005.

Boxplot

Outliers

Of the 12 scores identified to be outliers, 4 are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn   DFd     F     p p<.05   ges
## 1 baseline_number 3.28 252.5 0.789 0.511       0.005

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Baseline 5 Summary

Baseline 5 Histogram

Reaction Time

Three Baseline Tests

For individuals who completed three baseline tests (n = 2,390), performance on the reaction time composite score was statistically significantly different, F(1.97, 5,776.39) = 213.61, p < .0001, generalized eta squared = 0.03.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. All pairwise comparisons, between baseline test administrations, were statistically significantly different (p < .05). Individuals were identified to achieve their best reaction time score on the third baseline administration (M = 0.61) compared to the second (M = 0.62) and first (M = 0.65) baseline administrations. The difference in average performance between the first and second baseline administration was additionally significant.

Boxplot

Outliers

Of the 259 scores identified to be outliers, 47 are considered extreme.

Normality Assumption

From the plot, the extreme outliers appear to affect normality.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn     DFd       F        p p<.05   ges
## 1 baseline_number 1.97 5776.39 213.614 4.65e-89     * 0.028

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Four Baseline Tests

For individuals who completed four baseline tests (n = 420), performance on the reaction time composite score was statistically significantly different, F(2.78, 1,164.47) = 27.98, p < .0001, generalized eta squared = 0.03.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. Five out of six pairwise comparisons between baseline test administrations were statistically significantly different (p < .05). Individuals were identified to achieve their greatest reaction time score on the fourth baseline administration (M = 0.60) compared to the third (M = 0.62), second (M = 0.64) and first (M = 0.64) baseline administrations. The only non-significant comparison was between the first and second baseline administrations.

Boxplot

Outliers

Of the 55 scores identified to be outliers, 10 are considered extreme.

Normality Assumption

From the plot, the extreme outliers appear to affect normality.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn     DFd      F        p p<.05  ges
## 1 baseline_number 2.78 1164.47 27.981 2.08e-16     * 0.03

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Five Baseline Tests

For individuals who completed five baseline tests (n = 78), performance on the reaction time composite score was statistically significantly different, F(3.61, 277.92) = 10.56, p < .0001, generalized eta squared = 0.06.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. Six out of ten pairwise comparisons were statistically significantly different. Individuals were identified to achieve significantly greater reaction time scores on their third (M = 0.62), fourth (M = 0.61), and fifth (M = 0.60) baseline administrations compared to their first (M = 0.65) and second (M = 0.65) baseline administrations. Performance was not significanlty different between the first and second baseline administrations. It was additionally not significant between the third, fourth, and fifth baseline administrations.

Boxplot

Outliers

Of the 15 scores identified as outliers, 3 were considered extreme.

Normality Assumption

From the plot, the assumption of normality is threatened by extreme outliers on the second, fourth, and fifth baseline scores.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn    DFd      F        p p<.05   ges
## 1 baseline_number 3.61 277.92 10.558 1.91e-07     * 0.059

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Baseline 5 Summary

Baseline 5 Histogram

Visual Motor

Three Baseline Tests

For individuals who completed three baseline tests (n = 2,390), performance on the visual motor composite score was statistically significantly different, F(1.96, 5,745.48) = 1,959.31, p < .0001, generalized eta squared = 0.13.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. All pairwise comparisons, between baseline test administrations, were statistically significantly different (p < .05). Individuals were identified to achieve their best visual motor score on the third baseline administration (M = 39.54) compared to the second (M = 36.89) and first (M = 33.27) baseline administrations. The difference in average performance between the first and second baseline administration was additionally significant.

Boxplot

Outliers

Of the 99 scores identified to be outliers, none are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn     DFd        F p p<.05   ges
## 1 baseline_number 1.96 5745.48 1959.307 0     * 0.132

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Four Baseline Tests

For individuals who completed four baseline tests (n = 420), performance on the visual motor composite score was statistically significantly different, F(2.88, 1,208.07) = 266.59, p < .0001, generalized eta squared = 0.13.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. All six pairwise comparisons between baseline test administrations were statistically significantly different (p < .05). Individuals were identified to achieve their greatest reaction time score on the fourth baseline administration (M = 40.03) compared to the third (M = 38.25), second (M = 35.87) and first (M = 33.09) baseline administrations.

Boxplot

Outliers

Of the 19 scores identified to be outliers, none are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect  DFn     DFd       F         p p<.05   ges
## 1 baseline_number 2.88 1208.07 266.588 8.48e-129     * 0.134

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Five Baseline Tests

For individuals who completed five baseline tests (n = 78), performance on the visual motor composite score was statistically significantly different, F(4, 308) = 40.14, p < .0001, generalized eta squared = 0.13.

All possible pairwise comparisons were evaluated using the Bonferroni procedure to control family-wise Type I error. Seven out of ten pairwise comparisons were statistically significantly different. Individuals were identified to achieve significantly greater reaction time scores on their third (M = 37.47), fourth (M = 38.90), and fifth (M = 39.28) baseline administrations compared to their first (M = 32.30) and second (M = 35.08) baseline administrations. The difference between first and second baseline administrations was additionally significant. There were no significant differences between the third, fourth, and fifth baseline administrations.

Boxplot

Outliers

Of the 10 scores identified as outliers, none are considered extreme.

Normality Assumption

From the plot, normality is assumed.

ANOVA Computation

## ANOVA Table (type III tests)
## 
##            Effect DFn DFd      F        p p<.05   ges
## 1 baseline_number   4 308 40.144 4.65e-27     * 0.131

Pairwise Comparisons

Result Visualization

Baseline 1 Summary

Baseline 1 Histogram

Baseline 2 Summary

Baseline 2 Histogram

Baseline 3 Summary

Baseline 3 Histogram

Baseline 4 Summary

Baseline 4 Histogram

Baseline 5 Summary

Baseline 5 Histogram

ANOVA Summary

Overall, the results of the ANOVA calculations suggest individuals achieved higher scores on consecutive baseline testing across the verbal memory, visual memory, reaction time, and visual motor composite scores. Because of the differences in sample size across each group, there was more statistical power to identify significant differences in the testing performance of individuals who completed either three or four baseline test administrations.